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Magnetostriction plays a key role in magnetization dynamics inside soft magnetic materials, which are widely used in electronic devices for inductor cores. In general, the performance of the soft magnetic device is governed by magnetization dynamics such as domain-wall motions. Thus, it is indispensable to understand how magnetostriction affects the magnetization dynamics. We performed micromagnetic simulations in order to clarify the effects of the magnetostriction. To simulate the magnetostriction, we have to solve the elastic equations of the crystal structure.[1,2] The magnetization generates strains of the crystal structure, and deformations of the crystal are affected by the distant magnetization. We solved equations of motions for the strains, and we obtained the magnetostrictive field. We parallelized simulations using Message Passing Interface.[3] Figure 1 shows a simulation model containing two grains. Inside the grains, we consider strip-shape magnetic domains. The crystal axes are rotated -20 and 20 degrees from the x-direction in the grain A and B, respectively. We applied AC magnetic field along the x-direction. The frequency of the AC magnetic field is 100MHz. We also applied static external stress parallel to the crystal axis of the grain A. The magnetic material is Fe. Figure 2 shows energy losses as a function of the external stress using the simulation results. When the tensile strain is 20 MPa, the energy loss is 1.8 times larger than that without stress. The results of this work show that the energy loss strongly depends on the stress and the microstructure of the soft magnetic materials.References: [1] J.X. Zhang, and L.Q. Chen, Acta Materialia 53, 2845 (2005). [2] S. Bhattacharyya, T.W. Heo, K. Chang, and L.-Q. Chen, Modelling Simul. Mater. Sci. Eng. 19 035002 (2011). [3] H. Tsukahara, K. Iwano, C. Mitsumata, T. Ishikawa, K. Ono, Comput. Phys. Commun, 207, 217 (2016).

MMM 2020

Effects of magnetostriction on domain wall dynamics inside multi-grains soft magnet revealed by micromagnetic simulations

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

In the development of dedicated hardware for neuromorphic applications, the realization of suitable memristive devices as synaptic elements is a key factor. The main drawback of the existing devices is the reliability of the intermediate states and their scalability. In this study we propose a memristive device based on magnetic tunnel junctions (MTJ) and whose functionalities do not depend directly on the size of the device. The state of the memristor relates to the tunnel magnetoresistance (TMR) variation with the relative angle between the two in-plane magnetizations. The specificity of our concept consists in the integration of an isotropically coercive medium as magnetic free layer able to stabilize its magnetization along whatever in-plane direction. Here the current driven rotation of the magnetization is investigated on devices of 100nm of diameter. The spin transfer torque (STT) of the in-plane MTJ is considered together with the contribution of the additional perpendicularly magnetized polarizer. For a proper ratio of the two STT contributions, the magnetization switches from the parallel to the anti-parallel state following a circular out-of-plane trajectory as for the precessional switching [4]. We prove experimentally that by properly designing the voltage pulses we can discretely rotate and stabilize the magnetization along different in-plane directions, reaching an almost continuous range of intermediate resistances. The resistance variation turns out to be monotonous with the voltage polarity confirming the memristive behavior of the device under a train of pulses. A study on the thermal stability of the intermediate states shows a resistance variation below 2% for a 3min timescale. Moreover, the Joule effect, occurring during the application of pulses, adds a random contribution to the resistance jumps. The observed resistance noise is associated to the thermally activated switching of small magnetic areas of the samples, probably due to the granular nature of the sputtered samples. The larger the diameter, the lower the noise due to the increased number of grains.References: 1. Mansueto, M. et al. Phys. Rev. Appl. 12, 044029 (2019). 2. Mansueto, M. et al. 2020 IEEE International Memory Workshop (IMW) 1–4 (2020). 3. Mansueto, M. et al. in preparation 4. Vaysset, A. et al. Appl. Phys. Lett. 98, 242511 (2011)

Spintronic memristor based on the angular variation of TMR

Reservoir computing (RC) [1] is a subset type of recurrent neural network, where only the weights of the output layer are altered during training. This training scheme does not require multi-layer backpropagation and gradient descent, making RC simple to train. This technique is therefore well suited for resource constrained hardware environments, since expensive circuitry for updating internal reservoir weights is unnecessary. Some spintronic devices can exhibit highly nonlinear behavior that is extremely well-suited for implementing RC in hardware. We have proposed a novel reservoir comprising a planar arrangement of nanomagnets each having perpendicular magnetic anisotropy (PMA) [2]. Our solution differs from [3], which uses voltage pulses to move information within the reservoir, whereas ours uses the natural relaxation of the nanomagnets. Fig. 1(a) shows an example layout of nanomagnets with two input nanomagnets (A and B). The effect of nanomagnet magnetic fields upon adjacent nanomagnets exhibits two features: non-linear interaction and variable interaction strength, making the proposed implementation well-suited for RC. Information is input by stimulating individual nanomagnets or portions of the nanomagnet reservoir with external magnetic fields. The magnetizations of various nanomagnets are read electrically via magnetic tunnel junctions. A complementary single layer circuit is used to perform vector-matrix multiplication on the magnetization values and the trained output weights to obtain the output vector. Micromagnetic simulations are performed with MuMax3 for the nanomagnet network pictured in Fig. 1(a). The nanomagnet reservoir was simulated with an input stream comprising triangle or square waves. Fig. 1(b-d) shows various snapshots of the network during the simulation; colors indicate magnetization directions. Fig. 1(e) shows the reservoir inputs and outputs, and Fig. 1(f) tracks the magnetization over time for three nanomagnets. The reservoir successfully identified the waveforms with 100% accuracy for both the training and testing data.References: [1] H. Jaeger, Bonn, Germany: German National Research Center for Information Technology GMD Technical Report., Vol. 148, p.13 (2001) [2] P. Zhou, N. McDonald, A. Edwards, L. Loomis, C. Thiem, and J. Friedman. arXiv:cs.NE/2003.10948 (2020) [3] H. Nomura, T. Furuta, K. Tsujimoto, Y. Kuwabiraki, F. Peper, E. Tamura, S. Miwa, M. Goto, R. Nakatani, and Y. Suzuki. 2019, Japanese Journal of Applied Physics., Vol. 58, p.070901 (2019)

Reservoir Computing with Planar Nanomagnet Arrays

We experimentally demonstrate the application of superparamagnetic magnetic tunnel junctions (MTJs) in stochastic logic operations. The two resistance states of an MTJ are used as logical 1 and 0. When the energy barrier to magnetization reversal is low compared to the thermal energy, the MTJ switches between the 1 and 0 states stochastically. The MTJ resistance is instantaneously digital yet analog in time average. Spin transfer torque (STT) enables electronic control of the time averaged resistance [1]. Three 60 x 90 nm CoFeB MTJs were connected to the logical circuit, and their resistances were measured simultaneously (Figure 1(a)). The probabilities P of the eight possible microstates (x1,x2,y) were analyzed pairwise. We denote by (0,0) the state 000 that is consistent with the truth table of an AND gate together with 001 that is not. The preference for 001 relative to 000, C(x1=0,x2=0), was defined as the normalized difference between the probabilities P(001) and P(000). After connecting feedback, when, P(000) will increase and P(001) will become smaller, effectively decreasing C(0,0). The condition will be the same for C(0,1) and C(1,0) but not C(1,1), since P(111) increases but P(110) decreases. Figure 1(b) shows experimental results with the feedback connected, showing a statistical preference for valid AND gate states. Invertibility is based on what happens when the output is pinned to a particular value. Pinning y to 1 increases the probabilities for all the states with y = 1 (Figure 1(c)), while pinning y to 0 increases the probability for all the states with y = 0 (Figure 1(d)). This is qualitatively consistent with the energies of the different states.References: Bapna, M., & Majetich, S. A. (2017). Current control of time-averaged magnetization in superparamagnetic tunnel junctions. Applied Physics Letters, 111(24), 243107.

Superparamagnetic Tunnel Junctions for Invertible Stochastic Logic Gates

Emergent behaviours in complex systems arise from simple interactions between individual components that lead to global complexity [1]. Emergence is found in nature as a mechanism behind intelligent biological processes [2], but thus far, little has been done to exploit the computational power that emergence could offer for machine learning hardware. Here we demonstrate how the emergent properties of a magnetic system can be exploited to perform meaningful computation in materio. Using a combination of X-ray photoemission electron (X-PEEM) microscopy and polarised neuron reflectivity (PNR), we show that arrays of interconnected magnetic nanowire rings demonstrate emergence as a result of complex domain wall (DW) pinning events. The stochasticity associated with DW pinning produces emergent, dynamic equilibria in DW population and array magnetisation [3]. We then present a phenomenological model of these stochastic pinning events and show that the model provides excellent agreement to our experimental data (Fig. 2). The system’s nonlinear response and its inherent memory allowed us to implement a machine learning paradigm called ‘reservoir computing’ (RC). In RC, artificial neural networks are replaced by time-dependent ‘reservoirs’ which capture the advantages of recurrent neural networks (RNNs), without the associated difficulty of training RNNs [4]. Using the model, we demonstrated the feasibility of the ring arrays performing machine learning tasks, including speech processing and signal classification. We believe the sub-millimetre size and ability to solve complex tasks makes the arrays exciting candidates for microprocessors, with parallel computation and memory capability, enabling more energy efficient data processing tasks due to the reduced computational expense.References: [1] - P. Curseu, J. Inf. Technol., 21, (2006), [2] - B. Lindsey et al, Comprehensive Physiology, 2, (2012). [3] - R. Dawidek et al. [Under Review], [4] - M. Lukoševičius and H. Jaeger, Comput. Sci. Rev., 3, (2009).

Neuromorphic Computation Using Emergent Magnetisation Dynamics

The increasing demand of energy is requiring the continuous diversification of the production sources and the consideration of alternative potential resources such as the waste heat from industrial processes or residential heating systems. New devices and materials must be designed to recover efficiently the waste heat and among them, the thermomagnetic materials are an interesting alternative. The ideal thermomagnetic materials for energy harvesting devices should have a sharp ferro-paramagnetic phase transition, with minimal hysteresis and minimal latent heat and be accurately tuned to the available waste-heat temperature. The main objective of this work is to thoroughly investigate the thermomagnetic characteristics and their connection with the microstructural features for Fe79.7-xETMxNb0.3B20 (ETM = Cr, Mn; x = 11.5÷20 at.%) rapidly quenched alloys, depending on the ETM content. The possibility to tailor TC around room temperature and their minimal hysteresis recommends these glassy alloys for energy conversion applications. UHR-TEM studies indicate glassy structures with clusters of 2-3 nm embedded within an amorphous matrix. Mn additions double the saturation magnetization (80 emu/g) compared with Cr compositions (40 emu/g). The larger the ETM content (up to 20 at.%), the more reduced the Curie temperature is (from +450C down to -1000C). However, the Curie temperature is strongly dependent on the addition element. Mn is antiferromagnetic and behaves in a similar way as Cr does. Thus, the larger the Mn content the more numerous the antiferromagnetic interactions are, suggesting a transition temperature evolving more towards a Néel temperature for Mn contents over 16 at.%. Our aim is to study the complex interrelation among structure, mechanical, magnetic and thermal properties and, subsequently, to design new energy conversion devices with enhanced efficiency. Work supported by the Nucleu Programme (Project PN 19 28 01 01) and Contract No. 11PFE/16.10.2018 financed by the Romanian Ministry of Education and Research.

Fe-ETM-Nb-B (ETM = Cr, Mn) glassy alloys for energy recovery

Interacting nanomagnets with low thermal stability have been proposed for probabilistic computing, which has potential uses in low power sensing and logic, as well as in encryption and decryption [1]. Superparamagnetic tunnel junctions (SP-MTJs) are an ideal type of nanomagnet because their time-averaged magnetization of the free layer can be programmed with a voltage or current (Figure 1). We have previously used SP-MTJs for random number generation (RNG), and analog multiplication [2]. While voltage-controlled magnetic anisotropy (VCMA) has advantages for RNG due to ultra-low power consumption, spin transfer torque (STT) or spin orbit torque (SOT) is superior for logic devices due to the wider tuning range. For small sizes, magnetic tunnel junctions can be superparamagnetic near zero bias voltage, and the average retention time can be as short as a few hundred nanoseconds, so GHz speeds are feasible [3]. Pairs of superparamagnetic tunnel junctions fluctuate independently when isolated (Figure 2, top), but when coupled, the output of one is the NOT of the other (Figure 2, bottom). For AND and NAND gates the coupling between three SP-MTJs is optimized by Boltzmann machine simulations to statistically favor the set of microstates consistent with the truth table. Experimental results show that fast operation can be achieved with a hybrid SP-MTJ – CMOS circuit and without the need for a separate microprocessor. Prospects for optimizing the speed and performance of these devices will be discussed, and benchmarked with non-magnetic stochastic computing technologies.References: 1. K. Y. Camsari, et al., Phys. Rev. X 7, 031014 (2017). 2. M. Bapna and Sara A. Majetich, Appl. Phys. Lett. 111, 243107 (2017). 3. B. Parks, A. Abdelgawad, T. Wong, R.F. L. Evans, and S. A. Majetich, Phys. Rev. Applied 13, 014163 (2020).

Superparamagnets for Stochastic Computing INVITED

Two-dimensional MoSe is a multipurpose material that can be made into valleytronics and spintronic devices, quantum dots led, hydrogen evolution reaction catalyst, and ion-batteries. All the above functions are sensitive in any structural variation. The Cr-doped effect turns the MoSe2 from diamagnetism to paramagnetism. Room temperature Raman spectra show different behaviors between pure (x=0) and half Cr-doped (x=0.5) samples. The out-of-phase A1g vibration mode along c-axis of the crystal, shows an enhancement in the Crdoped MoSe2 but weaken in pure one. Both of two samples will return to their original status as magnetic field removed. In contrast, the applying external electric field broadening the FWHM of A1g mode in both samples and will not narrow down again as electric field removed. Furthermore, the Cr-doped MoSe2 also shows less influenced by the electric field. Varied-temperature x-ray diffraction (xrd) and Raman spectroscopy were studied. The temperature profile of xrd {002} peak position is associated with that's of the FWHM of A1g mode of Raman spectra. This observation shows how the MoSe2 interlayer's spacing influent the phonon softening behavior. The varied-temperature Raman spectra of MoSe2 sample display two peak broadening maxima of the A mode at Ta =150 K and Tb =220 K. Similar phenomena also appeared in Cr-doped one, but the Ta' and Tb' shifted to the higher temperature of 180 K and 260 K, respectively. This observation refers to both phonon softening temperatures are influent by Crdoped effect. As the 200 mT magnetic field applied, all of Ta , Tb , Ta' , and Tb' disappeared in both samples. The magnetic field reduces the phonon softening no matter Cr-doped or not. This study can be a reference for how the lattice and energy gap be affected under electric and magnetic filed as these materials are made as and electronic devices.References: 1. John R. Schaibley, Hongyi Yu, Genevieve Clark, Pasqual Rivera, Jason S. Ross, Kyle L. Seyler, Wang Yao & Xiaodong Xu, Nature Reviews Materials 1, 16055 (2016). 2. Wenwu Guo, Quyet Van Le, Amirhossein Hasani, Tae Hyung Lee, Ho Won Jang, Zhengtang Luo, and Soo Young Kim, Polymers 10, 1309 (2018). 3. Philipp Tonndorf, Robert Schmidt, Philipp Boettger, Rudolf Bratschitsch, Optics Express 21, 4908-4916 (2013). 4. Dahyun Nam, Jae-Ung Lee, and Hyeonsik Cheong, Scientific Reports 5, 17113 (2015).



Effect of magnetic and electric fields work on Cr-doped Mo1-xCrxSe2 (x=0, 0.5) nanosheet

Since the discovery of graphene, researches on two-dimensional (2D) materials have attracted much attention because of the good controllability of material properties. In 2018, 2D ferromagnetic metal Fe3GeTe2 devices have been developed [1], where the Curie temperature TC is originally 220 K and enhanced above room temperature by gating. In the next year, a cleavable ferromagnetic metal Fe5GeTe2 with TC = 310 K has been synthesized [2]. Although this material could be useful for future van der Waals (vdW) spintronic devices, magnetic properties of the thin Fe5GeTe2 films are not well established yet. In this work, we have fabricated thin film devices of both quenched (Q) and non-quenched (NQ) Fe5GeTe2 with various thicknesses and measured the Hall resistivities in a wide temperature range [3]. Figure 1 shows typical anomalous Hall effect (AHE) curves measured with both Q- and NQ- Fe5GeTe2 thin film (less than 10 atomic layer (L)) devices at T = 50 K. While any significant differences between Q and NQ devices have not been observed for thicker film (more than 10 L) devices (not shown here), the coercive field Hc of 5L Q-Fe5GeTe2 is about two times larger than that of 6L NQ-Fe5GeTe2. To investigate more details, we have plotted Hc as a function of temperature with both Q- and NQ-Fe5GeTe2 in Fig. 2. For comparison, Hc of thicker Q- and NQ-Fe5GeTe2 are also plotted. For all the devices, Hc starts to increase below 200 K, but the enhancement of Hc for thinner Q-Fe5GeTe2 can be clearly seen below 120 K, where one of the Fe atoms would be ferrimagnetically ordered. This work has demonstrated that the coercive field can be controlled by the film thickness and the synthesis method, and such a controllability of the perpendicular magnetic anisotropy should be useful for future vdW spintronic devices.References: [1] Y. Deng et al., Nature 563, 94 (2018). [2] A. F. May et al., ACS Nano 13, 4436 (2019). [3] T. Ohta et al., Appl. Phys. Express 13, 043005 (2020).

Enhancement of coercive field in van der Waals ferromagnet Fe5GeTe2

The recent discoveries of intrinsic ferromagnetism (FM) in two-dimensional (2D) dilute magnetic semiconductors with high Curie temperature (> 300 K) capable of spintronic applications are among the most impressive tour de force achieved by theoretical and experimental physicists in the field [1,2]. However, the origin of FM in these systems has remained an open issue. The power function proposed by Bloch, M(T) = M(0)[1 - (T/TC)α] with α = 3/2, has successfully described the temperature dependence of saturation magnetization MS(T) for bulk ferromagnetic materials [3]. The extended Bloch’s law for ferromagnetic nanoparticles (α-Fe) embedded in a non-magnetic matrix (SiO2) has yielded higher values of α associated with the reduced dimensionality effect [4]. In this study, we demonstrate that V doping into WS2 monolayer induces ferromagnetic couplings between the vanadium and its tungsten neighbors, forming nanosized ferromagnetic clusters that behave like ferromagnetic nanoparticles. The MS(T) dependence of the nanoclusters in V-WS2 monolayer samples with different V concentrations (0, 0.4, 2, and 8 at.%) is well described by the modified Bloch’s law at temperatures higher than the blocking temperature. Relative to the Bloch coefficient (α = 3/2), the higher values of α (up to 5.96) and its dopant concentration dependence reveal the dimensional effect and the magnetic interaction between the nanoclusters. This method has been successfully applied to describe the M(T) dependence of other 2D magnetic systems such as VSe2 monolayers that exhibit similar magnetic behavior. Our findings also offer a new way to predict the Curie temperatures of low-dimensional magnetic materials that may not be measured experimentally.References: 1. S. J. Yun, D. L. Duong, D. M. Ha, K. Singh, T. L. Phan, W. Choi, Y. M. Kim, Y. H. Lee, Adv. Sci. 7, 1903076 (2020). 2. F. Zhang, B. Y. Zheng, A. Sebastian, H. Olson, M. Z. Liu, K. Fujisawa, Y. T. H. Pham, V. J. Ortiz, V. Kalappattil, T. Zhang, R. Pendurthi, Y. Lei, A. Laura Elias, Y. Wang, P. E. Hopkins, S. Das, V. H Crespi, M. H. Phan, M. Terrones, Adv. Sci. 2020 (https://arxiv.org/abs/2005.01965) 3. F. Bloch, Z. Phys. 61, 206 (1930). 4. G. Xiao, C.L. Chien, J. Appl. Phys, 61, 8 (1987).

Extended Bloch’s law description of two-dimensional dilute magnetic semiconductors

Magneto-optical (MO) thin films can be used for applications in various ways such as MO microscopy, optical isolaters, and information storage devices. Although it is widely investigated, growth of high Faraday rotation magnetic thin films on glass substrate is still considered as a primary issue in MO thin films. Here, we have investigated enhancement of MO properties in praseodymium-substituted bismuth yttrium iron garnet (PrxBi1Y2-xFe5O12) thin film on a glass substrate by using a metallo-organic decomposition (MOD) method. To improve the MO performance of the as-prepared PrxBi1Y2-xFe5O12 thin film, different concentrations of Pr-substituted bismuth yttrium iron garnet were prepared. It shows that PrxBi1Y2-xFe5O12 thin film with an optimal concentration of x=1 exhibited high crystallinity, high saturation magnetization and the highest Faraday rotation (FR) angle of – 6.50/μm at a wavelength of 510 nm as shown in figure below. The Pr1Bi1Y1Fe5O12 thin film fabricated by the modified MOD method displayed excellent MO performance and is a potential candidate for application in optical devices.

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Effects of magnetostriction on domain wall dynamics inside multi-grains soft magnet revealed by micromagnetic simulations

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